WASHINGTON (AP) — In an election that may be decided on the strength of the American economy, President Barack Obama and Republican challenger Mitt Romney are looking to China to score political points as they compete for political support from working-class voters.

But both candidates also are taking some heat about their dealings with the communist superpower.

Republicans accuse Obama of failing to follow through on promises to crack down on China's trade policies. Democrats, meanwhile, raise questions about Romney's leadership of a private equity firm that invested in companies operating in China.

Beyond politics, there are real policy differences that could have a dramatic impact on the relationship between the United States and the country that is the largest foreign holder of U.S. Treasury debt.

Romney and Obama campaign officials set aside time at their respective political conventions to meet privately with China's ambassador to the United States. But publicly, both candidates are putting aside diplomatic niceties and talking tough.

The White House on Monday filed a complaint with the World Trade Organization over Chinese subsidies to its auto and auto parts industry, the latest in a series of actions dating back to 2009 to protest what U.S. manufacturers say are the unfair advantages China gives its own industries. The move came four days after Romney launched an advertising campaign accusing the president of allowing American manufacturing jobs to be lost to the Asian power.

At a campaign stop in Cincinnati, Obama charged that Romney made money from companies that outsourced jobs to China while running the private equity firm Bain Capital.

"You can't stand up to China when all you've done is send them our jobs," Obama said. "You can talk a good game. But I like to walk the walk, not just talk the talk. And my experience has been waking up every single day doing everything I can to make sure that American workers get a fair shot in the global economy."

Romney shot back in a statement accusing Obama of ignoring China for too long.

"Campaign-season trade cases may sound good on the stump, but it is too little, too late for American businesses and middle-class families," Romney said. "President Obama's credibility on this issue has long since vanished."

The issue hits home among working-class voters in manufacturing swing states such as Ohio, where Obama has gained recently in polls. And American voters don't seem to like China very much.

An NBC/Wall Street Journal poll conducted in July found that 62 percent of registered voters consider China more of an adversary, while just 25 percent see the country as an ally. About 86 percent of adults were at least somewhat concerned about how trade relations with China would impact the U.S. economy, Gallup found in February.

Romney is promising an aggressive course on China. In particular, he has vowed to issue an executive order in his first day in office labeling China a currency manipulator, a designation that would trigger negotiations between the two countries and could ultimately lead to U.S. trade sanctions against China.

The designation is opposed by the U.S. Chamber of Commerce and Jon Huntsman, the former GOP presidential candidate and onetime U.S. ambassador to China, who said it would spark a trade war that would damage U.S. businesses and threaten China's willingness to buy U.S. Treasury debt.

Complaining about China's manipulation of its currency is popular among both Democrats and Republicans, and it's a chorus Obama himself joined during his first run for the White House and has renewed since then. In a 2008 campaign position paper, Obama vowed to use "all diplomatic means" to put China's currency on a fairer footing.

But Obama has repeatedly refused to brand China a currency manipulator in a report that the Treasury Department is required to send to Congress twice a year. Past administrations also have been unwilling to take that step. China owns $1.16 trillion in U.S. Treasury securities, making it the largest foreign holder of Treasury debt.

But for now at least, Romney is not backing down. Over the weekend, he ran an advertisement across eight swing states accusing Obama of failing to crack down on China's behavior. And in his weekly podcast, Romney said that "in 2008, candidate Obama promised to take China 'to the mat.' But since then, he's let China run all over us."

Obama countered with a TV spot focused on Romney's past relationship with China. While Romney headed Bain Capital in the 1990s, the firm invested in several companies that operated in China. The Romney campaign has insisted that the Chinese-based factories did not supplant U.S. manufacturing jobs.

Much of the evidence is based on U.S. Securities and Exchange documents from that period, providing only sparse information on the China-based activities of these firms. But records do raise questions about what appear in some cases to be a broadening reliance on Chinese factories and workers by several firms targeted by Bain in the 1990s for investments and takeover bids.

Romney's posture on China's economic expansion was far less confrontational when he headed Bain Capital. In March 1998, while attending a forum on the future of U.S. cities, he extolled China's workplaces, which have in recent years come under fire for exploiting Chinese workers.

"I went to a factory of 5,000 workers making bread makers and so forth," said Romney, then the CEO of Bain. He said they were "working, working, working, as hard as they could, at rates of roughly 50 cents an hour. They cared about their jobs; they wouldn't even look up as we walked by."

On Monday, Romney called for a "crackdown on nations that cheat like China. That's killing jobs."